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Student[MultivariateCalculus]

  

DotProduct

  

return the dot product of two vectors

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

DotProduct(u, v, conjopt)

u . v

Parameters

u, v

-

Vectors with algebraic entries and equal dimensions

conjopt

-

(optional) a keyword argument of the form conjugate = truefalse; defaults to false

Description

• 

The DotProduct command computes the dot product of u and v.

• 

The infix operator . can also be used to compute the dot product.

• 

If u and v are n-dimensional Vectors, and conjugate is false, their dot product is given by the formula i=1nuivi. If conjugate is true, then their dot product is given by the formula i=1nui&conjugate0;vi.

Examples

withStudent:-MultivariateCalculus:

ua,b,c

uabc

(1)

vd,e,f

vdef

(2)

u.v

ad+be+cf

(3)

The complex dot product is not commutative.

DotProductu,v,conjugate=true

a&conjugate0;d+b&conjugate0;e+c&conjugate0;f

(4)

DotProductv,u,conjugate=true

d&conjugate0;a+e&conjugate0;b+f&conjugate0;c

(5)

Compatibility

• 

The Student[MultivariateCalculus][DotProduct] command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

Student

Student[MultivariateCalculus]